# MCT4C Mathematics for College Technology – Grade 12 (College)

PREREQUISITE: Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11, University Preparation

GRADE: 12 (College)

AVAILABILITY: Full-time – All Campuses, Private – All campuses, Blyth Academy Online

THE ONTARIO CURRICULUM: Mathematics

MCT4C online enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. MCT4C online prepares students for a variety of college technology programs.

### UNIT ONE

Polynomials Functions - Factoring and Solving- In this unit, students will learn to factor polynomials no higher than degree 4 and solve polynomial equations using factoring or the quadratic formula. Students will also learn how to expand polynomials and collect like terms to put polynomials in their simplest form.

### UNIT TWO

Polynomial Functions - Graphing Polynomials- In this unit, students will learn how to substitute and evaluate polynomial functions and recognize linear and quadratic polynomials and state their domain and range, degree, leading coefficient and the end behaviour. Students will learn how to identify cubic and quartic functions by equations or graphs, state the maximum number of x-intercepts, the domain and range and the end behaviour. Students will draw graphs of polynomials using zeros and end behaviour as well as estimate the zeros from a graph and determine their exact value using technology. Students will also learn to determine the equation of a polynomial (up to degree 4) given the graph or the zeros and another point.

### UNIT THREE

Polynomial Functions - Modelling with Polynomials- In this unit, students will solve problems related to real-world applications using polynomial functions and evaluate the reasonableness of the solution. Students will learn to read graphs and identify limitations on real-world applications using polynomial functions and solve for unknowns using formulas and rearrange formulas for specific values.

### UNIT FOUR

Exponential Functions- In this unit, students will evaluate powers and simplify algebraic expressions using laws of exponents and learn how to solve equations that involve exponents, both graphically and algebraically. Students will graph exponential equations with and without technology and use these graphs to estimate solutions to exponential equations. Students will also solve real-world applications that can be modelled by exponential equations and learn how to convert between exponential and logarithmic form and work with laws of logarithms to simplify expressions.

### UNIT FIVE

Trigonometric Functions- In this unit, students will use the primary trig ratios (sine, cosine and tangent) along with Sine Law and Cosine Law to calculate the lengths of sides and the values of angles and apply this to real-world examples. Students will learn to determine exact values of sine, cosine and tangent of special angles and solve for the missing angles given a trigonometric ratio.

### UNIT SIX

Graphing Trigonometric Functions- In this unit, students will draw the graphs of the sine and cosine functions in degrees and draw the graphs using transformations. Students will learn to determine the amplitude, period, phase shift and vertical translation of a sinusoidal function and use it to write the equation using sine and cosine. Students will also learn to write the trigonometric equations to model real-world applications and use these equations to solve problems.

### UNIT SEVEN

Geometry and Circle Geometry- In this unit, students will perform conversions within the metric system, the imperial system and between the two. Students will solve problems involving perimeter, area, surface area and volume. Students will also learn to determine circle properties and solve related problems, including those arising from real-world applications.

### UNIT EIGHT

Vectors- In this unit, students will learn how to distinguish between a vector and a scalar and be able to represent a vector in a variety of different ways. Students will learn how to resolve a vector into horizontal and vertical components, represent a vector as a directed line segment given horizontal and vertical components and determine the sum or difference of two vectors. Students will also calculate the sum or difference of two vectors and solve problems involving the addition and subtraction of vectors in problems arising from real-world applications.

### CULMINATING PROJECT

- This project is one of the final evaluations of MCT4C online. This project will challenge students to use the knowledge and skills gained throughout the course and is worth 10% of the final grade.

### FINAL EXAM

Proctored Exam- This exam is the final evaluation of MCT4C online. Students need to arrange their final exam 10 days in advance. All coursework should be completed and submitted before writing the final exam, please be advised that once the exam is written, any outstanding coursework will be given a grade of zero. The exam will be two hours. There are two options for taking the exam:
- WRITE EXAM AT BLYTH ACADEMY CAMPUS: If you live close to a Blyth Academy Campus, or if you attend a Blyth Academy Campus, you can take your exam there. Once inside the exam scheduling interface, please click Login/Create Account. Check for an available time and date at the campus of your choosing. The earliest available date will be open within the next 3-5 business days. You cannot book an exam in more than one campus or multiple times at the same campus. You will receive an automatic confirmation email with next steps and exam information. You can cancel and reschedule anytime using the same link.
- USE EXAMITY PROCTORING SERVICE: For a fee of 22 USD*, students can arrange to take their exam in the comfort of their own home, at any time, on any day. Please select Examity Exam in the exam section of your course to set up your Examity profile and schedule your exam. Exams must be scheduled at least 24 hours in advance. *Price is subject to change.
- Please email exams@blythacademyonline.com if you need assistance.